How important will statistical learning be to a conscious AI?
Computational Learning Theory gives us an interesting framework to understand what statistical learning is doing. 

The gist of it is, we can model the process of statistical learning as one of formal deduction. The learning itself does not require a random element.

This shouldn't be too surprising. Consider a classic decision tree learner like C4.5 or ID3: the algorithm works through the data deterministically, and no random decisions are made. When asked to make a prediction, the learned model returns the frequency of each possible label within the most similar subpopulation from its training data, with similarity defined according to the algorithm's rules for partitioning data.

There's no reason you can't write a decision tree learner (or even a deep learning algorithm) in Prolog, it just might not be very efficient, or very practical.